next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Points :: pointsByIntersection

pointsByIntersection -- computes ideal of point set by intersecting maximal ideals

Synopsis

Description

This function computes the ideal of a finite set of points by intersecting the ideals for each point. The coordinates of the points are the columns in the input matrix M.
i1 : M = random(ZZ^3, ZZ^5)

o1 = | 8 0 0 7 1 |
     | 2 8 6 8 7 |
     | 6 4 2 5 3 |

              3        5
o1 : Matrix ZZ  <--- ZZ
i2 : R = QQ[x,y,z]

o2 = R

o2 : PolynomialRing
i3 : pointsByIntersection(M,R)

               2                                  2                       
o3 = {8y*z - 9z  - x - 50y + 24z + 192, 8x*z - 11z  - 35x + 2y + 64z - 96,
     ------------------------------------------------------------------------
       2     2                                 2                           2
     8y  - 3z  + 5x - 86y - 8z + 256, 2x*y - 3z  - 17x - 16y + 34z + 40, 8x 
     ------------------------------------------------------------------------
          2                             3      2
     - 35z  - 43x - 14y + 224z - 224, 8z  - 75z  - 3x + 18y + 208z - 288}

o3 : List

See also

Ways to use pointsByIntersection :